Mathematics
Answer
In △ABC,
AB = AC
⇒ ∠B = ∠C = x ….(1) (let) (Angles opposite to equal sides in a triangle are equal)
In △BDC,
BD = CD
⇒ ∠DBC = ∠DCB = y ….(2) (let) (Angles opposite to equal sides in a triangle are equal)
Subtracting eq.(2) from (1), we have :
⇒ ∠B - ∠DBC = ∠C - ∠DCB
⇒ ∠ABD = ∠ACD
⇒ ∠ABD : ∠ACD = 1 : 1.
Hence, option 3 is the correct option.
Related Questions
In the adjoining figure, AB = AC and BD = CD. Then, ∠ADC =
60°
75°
90°
100°
In the adjoining figure, AB = AC, BD = CD, ∠BAD = 32°, ∠BDC = 56°, ∠CAD = 2x° and ∠BDA = (x + y)°. The values of x and y will be :
x = 10, y = 16
x = 16, y = 12
x = 18, y = 8
x = 12, y = 16
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then △ABC is congruent to:
△FED
△EFD
△DEF
△FDE
ABC is a right angled triangle whose hypotenuse is AC. If AB : BC = 3 : 4, then the smallest angle of the triangle is :
∠A
∠B
∠C
None of these